Eur. Phys. J. E (2013) 36: 18
https://doi.org/10.1140/epje/i2013-13018-y

Regular Article

Surface instability of a gel disc in swelling

CNRS and Institut Jean le Rond d’Alembert, UMR7190, Place Jussieu 4, Case 162, 75005, Paris, France

^* e-mail: pasquale.ciarletta@upmc.fr

Received: 28 November 2012
Accepted: 29 January 2013
Published online: 26 February 2013

Abstract

The swelling of a soft disc made of polymeric gel and attached to a fixed substrate is modeled using a variational method in nonlinear elasticity. A linear stability analysis is performed to detect the onset of a surface instability. An exact solution of the perturbed disc is found, and both the threshold values of the growth rates and the surface morphology are derived analytically.